Dynamics at Newtonian-FENE fluid interface

A combined lattice Boltzmann, lattice Fokker-Planck simulation of entrainment of a base viscoelastic layer by flow of overlying Newtonian fluid. Arrows show local fluid velocity and colors represent pressure. Vortices appear in the Newtonian fluid and behind waves in the viscoelastic layer.

Flexible plants, fungi and sessile animals reconfigure in wind and water to reduce the drag acting upon them. Our numerical and experimental results suggest that the three-dimensional cone shape of reconfigured leaves in addition to flexibility is significant to both the reduction of vortex-induced vibrations and the forces experienced. Read more...

This work, led by then-UNC-undergraduate Mandi Traud, explored the structure of Facebook friendships using the tools of community detection in networks. Combining computational advances with a simplified presentation of pair-counting statistics, we compare and contrast algorithmically-detected communities with different user attributes to explore the organizing factors of social lives at different universities. Read more...

The new fast multipole method is combined with an adaptive oct-tree structure to rapidly evaluate the Coulomb, Yukawa, and low frequency Helmholz potentials of N particles in three dimensions. Read more...

Normal stresses exerted by motion of a cilium depicted at various beat phases. The cilium exerts a net force propeling ambient fluid along positive x-direction due to asymmetry in cilium axoneme stiffness. Read more...

Quantifying the flows generated by the pulsations of jellyfish bells is crucial for understanding the mechanics and efficiency of their swimming and feeding. The pulsing kinematics and fluid flow around the benthic jellyfish Cassiopea spp. were investigated using a combination of videography, digital particle image velocimetry and direct numerical simulation. Read more...

Human learning requires flexibility to
adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two
attributes—flexibility and selection—must operate over multiple
temporal scales as performance of a skill changes from being slow
and challenging to being fast and automatic. Read more...

Spectral deferred corrections
are used as preconditioners to a Picard integral collocation formulation to solve initial value problems. The resulting Krylov deferred correction (KDC) methods are of arbitrary order of accuracy and very stable. Read more...

Settling of a solid sphere in stratified fluids at low Reynolds number

A montage of snapshots (taken 10s apart) of a solid sphere settling in a stratified highly viscous fluid (corn syrup). Lighter fluid (dyed green) is entrained by the sphere as it enters the lower, heavier (clear) fluid.

Aerosol trajectories in lung bifurcation flow

Non-spherical aerosols tumble and interact with lung airflow. Aerosol shape can be tuned to ensure preferential paths along one branch or the other of the bifurcation, behavior of interest in pharmaceutical delivery.

Insects that are 1 mm in length or less often clap their wings together at the end of each upstroke and fling them apart at the beginning of each downstroke. We use the immersed boundary method to simulate clap and fling in rigid and flexible wings. We find that the maximum drag force generated during the fling can be reduced by about 50% with the addition of flexibility.
Read more...

A generalized framework of network quality functions that allows study of the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows studies of community structure in a general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales. Read more...

Network graph analysis of sheared nano-rod composite properties

We use network graph and community detection methods on physical realizations of sheared nano-rod dispersions. These realizations are drawn from the PDF database of Ruhai Zhou from a Smoluchowski equation solver of liquid crystal polymer kinetic theory.

Mass transport in biphasic core-annular flow

Flow of mucus through lung airways is an important mechanism of lung functions. Mucus is propelled by airway wall cilia as well as air flow. This montage of images shows the motion of a layer of highly viscous silicone oil (emulating mucus) coating the inner wall of a vertical glass tube.

Escape and trapping of oil plumes in density stratified fluids

The escape and trapping of buoyant miscible plumes rising through strongly stratified fluids is shown here experimentally. This critical phenomenon is determined by the distance between plume release height and depth of ambient density transition.

Numerical simulation of a vortex ring propagating through a density stratified fluid

Dense core vortex rings moving downward through a stratified ambient fluid exhibit several critical phenomena. For the
parameters of this numerical simulation, the core of the vortex ring rebounds at the sharp ambient density transition fragmenting into chandelier-like pendants.

Surface Waves

Image of a surface wave propagating through the thirty-six meter long wave tank in the Joint Fluids Lab. This image was taken as part of a project conducted by communications professor, Francesca Talenti, and her students in a course on film and photography.

CCIAM

The Carolina Center for Interdisciplinary Applied Mathematics integrates research and educational activities in mathematics and its intimate ties with the physical, engineering, biological, medical, and social sciences. The Center focus is to bring the power of mathematics to bear on the most intriguing, challenging, and relevant problems of our time, in collaborations with colleagues at UNC and elsewhere. These activities and advances in mathematics and scientific computation are continuously folded into our undergraduate and graduate curriculum, and provide broad research opportunities and collaborations with CCIAM faculty, post-doctoral scholars, and students.

The Applied Mathematics Program was started in 1996 as a result of a UNC initiative to provide expertise in mathematical modeling and computational science for the campus, and to integrate this expertise into research collaborations and undergraduate and graduate training. The guiding concept of the program is to combine excellence in mathematics and computation with a fundamental interest and commitment to interdisciplinary science. This concept underlies all research and teaching activities.

CCIAM faculty are leaders in a wide range of core mathematics (ordinary, partial, and stochastic differential equations, dynamical systems, network and data science, asymptotic analysis, numerical methods, and scientific computation) and in the applications of core mathematics to fluid dynamics, material science, social science, astrophysics, and many areas of biology and biomedicine (cell, organismal, marine, immunology, drug delivery, physiology of the heart, lung, and brain, predictive modeling for surgery).

Anyone interested in educational and research opportunities is encouraged to contact CCIAM faculty individually or the Director.